Chapter 13.3, Problem 36E

To determine

To find:If the statement “a linear regression model with a positive correlation coefficient has a graph with a slope that is greater than 0” is true or false.

Answer to Problem 36E

The given statement is true based on the reason given below.

Explanation of Solution

Based on the value of the correlation coefficient, following 5 deductions are implied:

1) For $r=-1$ , there is a perfect negative correlation.

2) For $-1<r<0$ , the relation moves from strong to weak negative linear relationship.

3) For $r=0$ , there is no linear relationship.

4) For $0<r<1$ , the relation moves from weak to strong positive linear relationship.

5) For $r=1$ , there is a perfect positive correlation.

For a positive value of r, there is a positive linear relationship among the data points, that is, with the increase in the value of x, the value of y also increases producing a line with slope greater than 0.

Hence, the given statement is true.